This invention relates to accelerometers, in general, and more particularly to an improved resonator vibrating beam accelerometer which is of a monolithic construction.
Vibrating beam accelerometers have found widespread use in aircraft navigation systems. In a vibrating beam accelerometer, a proof mass is supported by a beam. This beam is caused to vibrate by exciting piezoelectric beam material with an oscillator circuit. In an axially unstressed condition, the beam has a certain natural frequency of vibration, determined primarily by its dimensions, the material of which it is made, temperature and the medium in which it is operating. In response to an axial stress applied to the beam, the natural frequency of vibration changes, the frequency increasing in response to axial tension and decreasing in response to axial compression. Such a vibrating beam accelerometer is described in U.S. Pat. No. 3,470,400. The device disclosed therein is a single beam device.
Although this worked reasonably well, it was discovered that there were advantages to utilizing two beams, one of which would be stressed in compression and one in tension. In such a case, two beams and two proof masses are arranged so that an input acceleration places one beam in tension and the other in compression. The output is then taken as the difference frequency between the two beams. Such an arrangement is disclosed in U.S. Pat. No. 3,479,536. The two beam mechanization is described by the following equations: Note that these equations express the frequency behavior of the individual beams as a power series. The K.sub.o terms are individual resonator bias (no load) frequency terms and the K.sub.1, K.sub.2, K.sub.3 are respectively the first, second and third order acceleration-frequency (a-f) sensitivities.
BEAM 1 OUTPUT (beam in tension) EQU f.sub.1 =K.sub.01 +K.sub.11 a+K.sub.21 a.sup.2 +K.sub.31 a.sup.3 . . . (1)
BEAM 2 OUTPUT (Beam in compression) EQU f.sub.2 =K.sub.02 -K.sub.12 a+K.sub.22 a.sup.2 -K.sub.32 a.sup.3 . . . (2)
DIFFERENCE FREQUENCY OUTPUT ##STR1##
The advantages which the dual beam push-pull mechanization gives includes the following:
The difference frequency and, hence, accelerometer bias, is low, the tolerance on the match of the individual beam bias K.sub.o will determine the difference bias. The scale factor will be twice that of the individual beam scale factor. The difference frequency a.sup.2 term is nominally zero to reduce vibration effects and increase linearity.
The diference frequency a.sup.3 term is nominally doubled, however, this term is small.
Differencing results in common mode rejection to greatly reduce thermal effects.
The common mode rejection obtained by differencing greatly reduces the effect of bias error sources that affect both the individual beams in a similar manner, such as thermal effects and aging. Thus, for all of these reasons, a dual beam mechanization which uses the difference frequency between one beam in tension and the other beam in compression is an essential requirement in a vibrating beam accelerometer to meet present-day requirements.
FIG. 1 shows a prior art vibrating beam accelerometer having one beam in tension and one beam in compression. There is thus, for each of the two accelerometer portions a housing 11. Within each housing is a proof mass 13 supported by a flexure 15 with the other side of the flexure having a part 17 embedded into the housing 11. The proof masses 13a and 13b are supported, respectively, by beams 19a and 19b. Beam 19a is in tension for an input acceleration in the direction of arrow 21, and beam 19b in compression. The structure which includes the beam is a piezoelectric structure and also includes on each end of the beam an isolator mass 23 and a pair of isolator springs 25. One end of the beam structure, indicated generally as 27, is connected to the housing 11 and the other end to the proof mass 13a or 13b. This, then, is the general arrangement of the prior art type device. The problem with this device is that there are a total of three joints needed to make the assembly. There is the joint between the beam structure 27 and the housing 11, the joint between this structure 27 and the proof mass 13a or 13b and the joint between the proof mass part 17 and the housing 11. Typically, in the prior art, both the housing 11 and proof mass 13a or 13b are made of metal and the structure 27, of quartz. The joints between the resonator and housing and resonator and proof mass are made using an epoxy. This epoxy has a relatively large thermal expansion coefficient compared to that of the metal pieces. Because of this difference in thermal expansion coefficient, stresses occur in the joints when the parts experience a temperature change. The epoxy, being an inorganic material, responds to these stresses by exhibiting plastic-like strains. These plastic-like strains may take place over a long periods of time and result in a creep type of behavior of the joint. This joint creep instability results in minute geometrical relationship changes between the quartz resonator and metal parts. This in turn, changes the boundary conditions of the vibrating beam, which results in a change in bias (no load) frequency. The changes in boundary condition enhanced frequency must be limited to on the order of a few parts in 10.sup.9 for the accelerometer to have good bias stability. Due to the creep instability of the joints, the vibrating beam accelerometer experiences undesirable bias strains over a period of time.
It is, thus, the object of the present invention to overcome these difficulties by providing a dual beam vibrating beam accelerometer which has a monolithic resonator and proof mass flexure, monolithic meaning that the resonator and flexure will be made of a single piece of quartz, thereby avoiding the joints which are the cause of the creep problem in the prior art.